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Dynamic Monetary Risk Measures for Bounded Discrete-Time Processes

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Dynamic Monetary Risk Measures for Bounded Discrete-Time Processes
2.	Creator	Author's name, affiliation, country	Patrick Cheridito; Princeton University, USA
2.	Creator	Author's name, affiliation, country	Freddy Delbaen; ETH Zürich, Switzerland
2.	Creator	Author's name, affiliation, country	Michael Kupper; ETH Zürich, Switzerland
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)
4.	Description	Abstract	We study dynamic monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a dynamic risk measure time-consistent if it assigns to a process of financial values the same risk irrespective of whether it is calculated directly or in two steps backwards in time. We show that this condition translates into a decomposition property for the corresponding acceptance sets, and we demonstrate how time-consistent dynamic monetary risk measures can be constructed by pasting together one-period risk measures. For conditional coherent and convex monetary risk measures, we provide dual representations of Legendre--Fenchel type based on linear functionals induced by adapted increasing processes of integrable variation. Then we give dual characterizations of time-consistency for dynamic coherent and convex monetary risk measures. To this end, we introduce a concatenation operation for adapted increasing processes of integrable variation, which generalizes the pasting of probability measures. In the coherent case, time-consistency corresponds to stability under concatenation in the dual. For dynamic convex monetary risk measures, the dual characterization of time-consistency generalizes to a condition on the family of convex conjugates of the conditional risk measures at different times. The theoretical results are applied by discussing the time-consistency of various specific examples of dynamic monetary risk measures that depend on bounded discrete-time processes.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2006-01-26
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/302
10.	Identifier	Digital Object Identifier	10.1214/EJP.v11-302
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 11
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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